Problem: All of Emily's friends wanted to try the candy bars she brought back from her trip, but there were only 21 candy bars. Emily decided to cut the candy bars into pieces so that each person could have $\frac{7}{8}$ of a candy bar. After cutting up the candy bars, how many friends could Emily share her candy with?
We can divide the number of candy bars ( $21$ ) by the amount Emily gave to each person ( $\frac{7}{8}$ of a bar) to find out how many people she could share with. $ \dfrac{{21 \text{ candy bars}}} {{\dfrac{7}{8} \text{ bar per person}}} = {\text{ total people}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of $\dfrac{7}{8} \text{ bar per person}$ is ${\dfrac{8}{7} \text{ people per bar}}$ $ {21\text{ candy bars}} \times {\dfrac{8}{7} \text{ people per bar}} = {\text{total people}} $ ${\dfrac{168}{7}\text{ people}} = 24\text{ people}$ By cutting up the candy bars, Emily could share her candy with 24 of her friends.